The molecular mechanisms governing internal fluctuations in intrinsically disordered protein (IDP) assemblies are crucial to the stability and dynamics of both regulated and aberrant toxic cellular aggregates, but remain poorly understood. By comprehensively combining high-resolution quasi-elastic neutron scattering with all-atom molecular dynamics simulations, we probe the motions of D-casein, a model IDP, inside its assemblies. We uncover a previously unresolved slow relaxation process with phenomenological characteristics of anomalous non-Fickian diffusion. This anomalous signature emerges from a continuous mobility gradient governed by density and crowding within the assemblies; the core is denser and more compact, and mobility increases progressively toward the exterior. This dynamical heterogeneity underlies the non-Gaussian behavior and accounts for the observed spectral broadening. Our findings provide insight into how disorder and extreme local crowding within IDP assemblies can result in a fundamentally different behavior compared to, e.g., clusters of well-folded proteins. The deviations from Fickian diffusion arise from dynamic heterogeneity and can be captured within the framework by a model typically used for the jump diffusion observed in liquids, thereby extending its applicability.